Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical review. B, Condensed matter

Coherent signature of differential transmission signals in semiconductors: Theory and experiment

Georg Bartels, G. C. Cho, T. Dekorsy, H. Kurz, A. Stahl, Klaus Köhler

Published Jun 15, 1997• 65 citations
Publisher

Abstract

Transient pump-probe signals of a GaAs/${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As quantum well are investigated both theoretically and experimentally for different excitation conditions. The calculations are based on a microscopic density-matrix approach taking higher-order correlations into account. We present spectrally resolved transients which provide insights into the nature of the differential transmission change. Especially the complex phase signature of heavy-hole--light-hole quantum beats in dependence of the detection energy allows for an identification of different microscopic processes in the pump-probe signal. The theoretical results are verified experimentally by comparison with the coherent and incoherent parts of the time-resolved data. We find a dominant role of the Coulomb-induced correlations up to the ${\mathrm{\ensuremath{\chi}}}^{(3)}$ relevant four-point level in the coherent signature in comparison to the Pauli blocking contributions.

DOI
10.1103/physrevb.55.16404

Related papers

Coherent effects in spectrally resolved pump-probe differential reflectivity measurements at exciton resonance in GaAs quantum wells

Bipul Pal, Arvind S. Vengurlekar

We perform femtosecond spectrally resolved pump-probe differential reflectivity measurements on excitons in GaAs quantum wells in both coherent and incoherent regimes. The spectral signal is nonzero and oscillatory at $\ensuremath{-}\mathrm{ve}$ delay up to a few ps indicating persistent coherence between excitonic polarization induced by the probe pulse and the delayed pump pulse. The signal for small $+ve$ and $\ensuremath{-}\mathrm{ve}$ delay $(\ensuremath{\tau})$ shows modulation caused by quantum beats due to coexcitation of heavy and light hole excitons. The rise of the signal with $\ensuremath{\tau}$ for $\ensuremath{\tau}<0$ is rather nonexponential and is sensitive to detuning of the detection energy with respect to the exciton energy. The signal decay with $\ensuremath{\tau}$ for small $+ve$ $\ensuremath{\tau}$ shows dependence on pump-probe relative polarization. The excitonic reflectivity shows a large reduction caused by excitonic absorption saturation for both $+ve$ and $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}$ when the pump pulse intensity is increased to large values. To compare the experimental results with theory, we obtain an expression for the PPDR signal in terms of the third order excitonic polarization. This has an additional term not considered earlier to describe pump-probe experiments. The calculations are performed using optical Bloch equations, modified to incorporate exciton inhomogeneous broadening, quantum beats, and many body effects such as local field, excitation induced energy shift, and dephasing. These effects are found essential in explaining the observed PPDR spectral data. The delay dependence of the signal near the exciton energy is mainly controlled by inhomogeneous broadening for $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}.$ The signal decay for large $+ve$ $\ensuremath{\tau}$ has an exponential behavior determined by the lifetime of incoherent excitons. Experiments for collinear polarization reveal an additional exponential component for small $+ve$ delay. Theoretically, this is found to be related to exciton dephasing and is present only when many body effects are included.

Physical review. B, Condensed matter•Sep 10, 2003•9 citations

Discrimination between the Interband and Intraband Coherences in Pump-Probe Signals from Semiconductors

Georg Bartels, A. Stahl

We discuss coherent heavy-hole light-hole quantum beats in transient pump–probe signals from a homogeneous GaAs quantum well in the low density regime using a microscopic density matrix theory. A key feature of our theory is the inclusion of higher order correlation functions like the biexciton transition amplitude and the exciton density comprising both interband and intraband character. Our calculations show that the heavy-hole light-hole quantum beats are dominated by the longer living intraband coherent contributions for most excitation conditions. In the special case when both pump and probe are linearly polarized, forming an angle of 45°, the coherent signature is exclusively caused by the otherwise small contributions of the biexciton transition amplitude, i.e. an interband coherent correlation function. In this way the different interband and intraband dephasing times should be observable separately in PP signals, depending on the excitation conditions.

physica status solidi (b)•Mar 1, 1998•7 citations

Many-body effects in low-order optical nonlinearities of semiconductor quantum wells

Ilia Roumiantsev

This dissertation addresses both fundamental aspects of Coulomb correlations in semiconductor quantum wells and more practical aspects of theoretical analysis of semiconductor optoelectronic devices. After introducing the subject, we present and evaluate a state-of-the-art theory of the third order coherent optical response of a semiconductor quantum well based on the Dynamics Controlled Truncation (DCT) scheme. Already in the third order (the so-called chi (3)) regime, semiconductors exhibit a number of many-body Coulomb correlation effects. Their manifestation in various multi-pulse experimental configurations, customarily used in ultrafast semiconductor spectroscopy, has been an important component of this thesis. Coherent optical effects in a semiconductor 3-band system based on the heavy-hole, light-hole and conduction bands were investigated. The quantum beats in the time-integrated differential transmission signal were analyzed and compared with experimental data obtained at the University of Iowa. Fundamental differences from corresponding quantum beats in atomic 3-level systems were found. Also, the analysis of experimental data (obtained at the University of Arizona) of the coupled heavy-hole-light-hole optical Stark shift revealed evidence of intervalence band coherences, an analog of Raman coherences in atomic 3-levels systems. A scheme for realization of electromagnetically-induced transparency (EIT) based on the interference of excitonic and biexcitonic coherences was proposed. Corresponding experiments performed at the University of Oregon showed indeed a considerable coherent reduction of excitonic absorption. Furthermore, an extension of the chi(3) analysis revealed an energy renormalization of the biexciton, in good agreement with the corresponding experiment. A microscopic analysis of polarization dynamics in time-resolved four-wave mixing signals was performed, revealing interesting implications for the biexciton dephasing in addition to the significance of many-body correlations. In the case of four-wave mixing in semiconductor microcavities, our theoretical analysis in conjunction with experimental data obtained at the University of Tokyo gave us indications for a significant shortcoming of the second Born approximation (2nd BA) applied to two-exciton Coulomb correlations in a thin semiconductor quantum well, in agreement with the general knowledge of the qualitative failure of the 2nd BA in systems with short-range interaction in two dimensions. We also analyzed a novel all-optical switching technique based on the nonlinear polarization rotation. Apart from identifying the many-particle processes relevant for the switch operation in the chi(3) regime, we proposed ways to further optimize the switch.

•Jan 1, 2003•0 citations

Probing Heavy-Hole and Light-Hole Excitonic Beats in a GaAs Quantum well with Phase-Locked Raman Pulse Pairs

Timothy M. Sweeney, Thomas Baldwin, Hailin Wang

Transient pump-probe studies using phase-locked Raman pulse pairs as the pump reveal a new interpretation for the heavy-hole and light-hole excitonic beats in transient differential transmission of a GaAs quantum well.

Conference on Lasers and Electro-Optics•Jan 1, 2010•0 citations

Ultrafast phase dynamics of coherent emission from excitons in GaAs quantum wells

D. S. Chemla, J.‐Y. Bigot, Mary‐Ann Mycek +2 more

We investigate the temporal evolution of the instantaneous frequency of ultrashort-pulse four-wave mixing in GaAs/${\mathrm{Ga}}_{\mathit{x}}$${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum-well structures. We find that the coherent light emitted by excitons exhibits a complex phase behavior which depends critically on the density of excitons and the central frequency of the exciting pulses. Depending on the excitation conditions, we observe nonlinear shifts of the instantaneous frequency within one ultrashort pulsed emission or quantum beats. In the latter case we determine that the beat \ensuremath{\pi}-phase shift is very fast, only 40% above the fundamental quantum limit. We also present elaborate numerical simulations of the experiments based on a six-band generalization of the semiconductor Bloch equations. This formalism takes into account Coulomb many-body interactions and Pauli exclusion. It reproduces the salient features of the experimental data. It fails to account for important details revealed by the very sensitive phase measurements. The discrepancies can be traced back to two approximations in the theory: the statical treatment of screening, and the Lorentzian description of dephasing. In both cases, this indicates the need for theoretical refinements requiring a microscopic description of Coulomb scattering and dephasing processes in a non-Markovian theory.

Physical review. B, Condensed matter•Sep 15, 1994•83 citations

Quantum Coherence of Continuum States in the Valence Band of GaAs Quantum Wells

T. Dekorsy, A. M. T. Kim, G. C. Cho +5 more

Quantum beats of heavy and light holes in GaAs quantum wells are investigated in femtosecond time-resolved four-wave mixing and transmission experiments as a function of optical excitation energy. Under nonexcitonic excitation conditions, the four-wave mixing signal disappears due to the immediate loss of the interband coherence of continuum states. In the transmission experiment, the quantum beats are observed up to excess energies of 75 meV above the exciton resonances. The experimental data clearly demonstrate the coherence of continuum states in the valence band. Changes of the beat frequency with the excitation energy are due to the dispersion of the valence bands.

Physical Review Letters•Sep 30, 1996•20 citations
Transient pump-probe signals of a GaAs/{\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}As quantum well are investigated both theoretically and experimentally for different excitation conditions. The calculations are based on a microscopic density-matrix approach taking higher-order correlations into account. We present spectrally resolved transients which provide insights into the nature of the differential transmission change. Especially the complex phase signature of heavy-hole--light-hole quantum beats in dependence of the detection energy allows for an identification of different microscopic processes in the pump-probe signal. The theoretical results are verified experimentally by comparison with the coherent and incoherent parts of the time-resolved data. We find a dominant role of the Coulomb-induced correlations up to the \ensuremathχ(3){\mathrm{\ensuremath{\chi}}}^{(3)}\ensuremathχ(3) relevant four-point level in the coherent signature in comparison to the Pauli blocking contributions.
We perform femtosecond spectrally resolved pump-probe differential reflectivity measurements on excitons in GaAs quantum wells in both coherent and incoherent regimes. The spectral signal is nonzero and oscillatory at $\ensuremath{-}\mathrm{ve}$ delay up to a few ps indicating persistent coherence between excitonic polarization induced by the probe pulse and the delayed pump pulse. The signal for small +ve+ve+ve and $\ensuremath{-}\mathrm{ve}$ delay $(\ensuremath{\tau})$ shows modulation caused by quantum beats due to coexcitation of heavy and light hole excitons. The rise of the signal with $\ensuremath{\tau}$ for $\ensuremath{\tau}<0$ is rather nonexponential and is sensitive to detuning of the detection energy with respect to the exciton energy. The signal decay with $\ensuremath{\tau}$ for small +ve+ve+ve $\ensuremath{\tau}$ shows dependence on pump-probe relative polarization. The excitonic reflectivity shows a large reduction caused by excitonic absorption saturation for both +ve+ve+ve and $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}$ when the pump pulse intensity is increased to large values. To compare the experimental results with theory, we obtain an expression for the PPDR signal in terms of the third order excitonic polarization. This has an additional term not considered earlier to describe pump-probe experiments. The calculations are performed using optical Bloch equations, modified to incorporate exciton inhomogeneous broadening, quantum beats, and many body effects such as local field, excitation induced energy shift, and dephasing. These effects are found essential in explaining the observed PPDR spectral data. The delay dependence of the signal near the exciton energy is mainly controlled by inhomogeneous broadening for $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}.$ The signal decay for large +ve+ve+ve $\ensuremath{\tau}$ has an exponential behavior determined by the lifetime of incoherent excitons. Experiments for collinear polarization reveal an additional exponential component for small +ve+ve+ve delay. Theoretically, this is found to be related to exciton dephasing and is present only when many body effects are included.
We discuss coherent heavy-hole light-hole quantum beats in transient pump–probe signals from a homogeneous GaAs quantum well in the low density regime using a microscopic density matrix theory. A key feature of our theory is the inclusion of higher order correlation functions like the biexciton transition amplitude and the exciton density comprising both interband and intraband character. Our calculations show that the heavy-hole light-hole quantum beats are dominated by the longer living intraband coherent contributions for most excitation conditions. In the special case when both pump and probe are linearly polarized, forming an angle of 45°, the coherent signature is exclusively caused by the otherwise small contributions of the biexciton transition amplitude, i.e. an interband coherent correlation function. In this way the different interband and intraband dephasing times should be observable separately in PP signals, depending on the excitation conditions.
This dissertation addresses both fundamental aspects of Coulomb correlations in semiconductor quantum wells and more practical aspects of theoretical analysis of semiconductor optoelectronic devices. After introducing the subject, we present and evaluate a state-of-the-art theory of the third order coherent optical response of a semiconductor quantum well based on the Dynamics Controlled Truncation (DCT) scheme. Already in the third order (the so-called chi (3)) regime, semiconductors exhibit a number of many-body Coulomb correlation effects. Their manifestation in various multi-pulse experimental configurations, customarily used in ultrafast semiconductor spectroscopy, has been an important component of this thesis. Coherent optical effects in a semiconductor 3-band system based on the heavy-hole, light-hole and conduction bands were investigated. The quantum beats in the time-integrated differential transmission signal were analyzed and compared with experimental data obtained at the University of Iowa. Fundamental differences from corresponding quantum beats in atomic 3-level systems were found. Also, the analysis of experimental data (obtained at the University of Arizona) of the coupled heavy-hole-light-hole optical Stark shift revealed evidence of intervalence band coherences, an analog of Raman coherences in atomic 3-levels systems. A scheme for realization of electromagnetically-induced transparency (EIT) based on the interference of excitonic and biexcitonic coherences was proposed. Corresponding experiments performed at the University of Oregon showed indeed a considerable coherent reduction of excitonic absorption. Furthermore, an extension of the chi(3) analysis revealed an energy renormalization of the biexciton, in good agreement with the corresponding experiment. A microscopic analysis of polarization dynamics in time-resolved four-wave mixing signals was performed, revealing interesting implications for the biexciton dephasing in addition to the significance of many-body correlations. In the case of four-wave mixing in semiconductor microcavities, our theoretical analysis in conjunction with experimental data obtained at the University of Tokyo gave us indications for a significant shortcoming of the second Born approximation (2nd BA) applied to two-exciton Coulomb correlations in a thin semiconductor quantum well, in agreement with the general knowledge of the qualitative failure of the 2nd BA in systems with short-range interaction in two dimensions. We also analyzed a novel all-optical switching technique based on the nonlinear polarization rotation. Apart from identifying the many-particle processes relevant for the switch operation in the chi(3) regime, we proposed ways to further optimize the switch.
We investigate the temporal evolution of the instantaneous frequency of ultrashort-pulse four-wave mixing in GaAs/Gax{\mathrm{Ga}}_{\mathit{x}}Gax​${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum-well structures. We find that the coherent light emitted by excitons exhibits a complex phase behavior which depends critically on the density of excitons and the central frequency of the exciting pulses. Depending on the excitation conditions, we observe nonlinear shifts of the instantaneous frequency within one ultrashort pulsed emission or quantum beats. In the latter case we determine that the beat \ensuremath{\pi}-phase shift is very fast, only 40% above the fundamental quantum limit. We also present elaborate numerical simulations of the experiments based on a six-band generalization of the semiconductor Bloch equations. This formalism takes into account Coulomb many-body interactions and Pauli exclusion. It reproduces the salient features of the experimental data. It fails to account for important details revealed by the very sensitive phase measurements. The discrepancies can be traced back to two approximations in the theory: the statical treatment of screening, and the Lorentzian description of dephasing. In both cases, this indicates the need for theoretical refinements requiring a microscopic description of Coulomb scattering and dephasing processes in a non-Markovian theory.
Quantum beats of heavy and light holes in GaAs quantum wells are investigated in femtosecond time-resolved four-wave mixing and transmission experiments as a function of optical excitation energy. Under nonexcitonic excitation conditions, the four-wave mixing signal disappears due to the immediate loss of the interband coherence of continuum states. In the transmission experiment, the quantum beats are observed up to excess energies of 75 meV above the exciton resonances. The experimental data clearly demonstrate the coherence of continuum states in the valence band. Changes of the beat frequency with the excitation energy are due to the dispersion of the valence bands.